How to Make It
Preheat oven to 425°F. Toss carrots and onion with 3 tablespoons oil and ½ teaspoon each salt and pepper on a rimmed baking sheet. Roast until beginning to soften, 12 to 14 minutes.
Meanwhile, heat remaining 1 tablespoon oil in a large skillet over medium-high. Season pork with remaining 1 teaspoon salt and ½ teaspoon pepper. Cook, turning occasionally, until browned on all sides, 6 to 8 minutes. Move vegetables to edges of baking sheet; place pork in center (reserve skillet). Roast until a thermometer inserted in center of pork registers 140°F, 10 to 12 minutes. Transfer pork to a cutting board; let rest for 5 minutes.
Add broth to skillet; cook over medium-high until liquid is reduced by half, about 3 minutes. Remove from heat and whisk in butter, tarragon, and mustard. Thinly slice pork and serve with vegetables and mustard sauce.